The Complexity of Antidifferentiation

Abstract

We consider real-valued functions defined on the interval [0, 1]. We denote by Δ the set of derivatives; i.e., ƒ Є Δ iff there is a differentiable function F such that F' = ƒ. Any such F is a primitive of ƒ and is uniquely determined up to a constant. To normalize, we denote by F(x)=ƒ^x_0ƒ the primitive determined by F(0)=0. This is the original Newtonian concept of integration as antidifferentiation.

Additional details